The zeros of the function h(r) = r² + 11r - 26 are r = -13, r = 2 and the vertex is (-11/2, -225/4).
What are the zeros and vertex of the function?Given the function in the question:
h(r) = r² + 11r - 26
To find the zeros of the function h(r) = r² + 11r - 26, we need to solve the equation h(r) = 0.
Using factoring:
r² + 11r - 26 = 0
Find two numbers whose sum is 11 and whose product is -26.
The numbers are -2 and 13.
Factor the equation:
(r - 2)(r + 13) = 0
Hence:
r - 2 = 0 and r + 13 = 0
Therefore, smaller r = -13, larger r = 2.
Next, we determine the vertex of the function:
Using the formula for the x-coordinate of the vertex, which is given -b/2a.
Here, the coefficient of r² is 1 (a = 1),
The coefficient of r is 11 (b = 11).
Substituting these values into the formula, we get:
r = -b/2a
= -11/( 2×1 )
= -11/2
The x-coordinate of the vertex is -11/2.
To find the y-coordinate, we can substitute r = -11/2 value back into the function:
h(r) = r² + 11r - 26
h(-11/2) = (-11/2)² + 11(-11/2) - 26
= 121/4 - 121/2 - 26
= 121/4 - 242/4 - 104/4
= (121 - 242 - 104)/4
= -225/4
Therefore, the vertex is (-11/2, -225/4).
Learn more about quadratic equations here:https://brainly.com/question/4038687
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Use >,<, or = to solve
the inequality below.
4/5 1/2
Answer:
4/5 > 1/2
Step-by-step explanation:
4/5 1/2
\/
4/5 -> 8/10
1/2 -> 5/10
\/
8/10 > 5/10
\/
4/5 > 1/2
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
4/5>1/2
Step-by-step explanation:
To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:
4/5 = 0.8
1/2 = 0.5
Then, we compare the two decimal numbers to get the answer.
0.8 is greater than 0.5.
Therefore, 4/5 is greater than 1/2
8. Paula needs to replace the floor in her family room since her cat peed in several
places. She wants to put down both vinyl flooring and carpet in the room. The
carpet she selected costs $2 per square foot. The vinyl floor covering costs $1
per square foot. She has $500 to spend on materials and must cover an area of
300 square feet. How much carpet and vinyl flooring will she buy to meet her
requirements?
Multiply. −2(−5)(−3)
Answer: -30
Step-by-step explanation:
-2 X -5 = 10
10 X -3 = -30
Therefore, -2(-5)(-3) = -30
The multiplication of −2(−5)(−3) is -30
The multiplication of numbers in brackets with negative signs takes a method whereby the signs are taken into account when performing the arithmetic operation.
From the given question, we are to multiply:
= - 2 × (-5) × (-3)
= +10 × (-3)
= -30
Learn more about the multiplication of numbers here:
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Janessa recently increased the size of his Jeep tires from the original P230/85R18 to the larger P250/85R21. If Janessa didn’t recalibrate her odometer, how far did she really travel on the new tires when her odometer shows she has traveled 23425 miles?
The distance Janessa traveled on the new tires with the given size is 26,470.25 miles.
The given parameters:
Original size of the tire, = P230/85R18The width of the smaller tire, = 230 mmAspect ratio, = 85%Larger size of the tire, = P250/85R21The width of the larger tire, = 250 mmAspect ratio, = 85%Reading of the odometer = 23,425 milesThe diameter of the smaller tire is calculated as follows;
[tex]0.85 = \frac{h}{230} \\\\h = 0.85 \times 230 \\\\h = 195.5 \ mm\\\\h = 195.5 \ mm \times \frac{1 \ in}{25.4 \ mm} \\\\h = 7.7 \ in[/tex]
diameter of the smaller tire;
D = 2(7.7 in) + 18 in
D = 33.4 in
The circumference of the smaller tire;
[tex]C_1 = \pi D\\\\C_1 = 3.142 \times 33.4 \\\\C_1 = 104.94 \ in[/tex]
The diameter of the larger tire is calculated as follows;
[tex]0.85 = \frac{h}{250} \\\\h = 0.85 \times 250 \\\\h = 212.5 \ mm\\\\h = 212.5 \ mm \times \frac{1 \ in}{25.4 \ mm} \\\\h = 8.37 \ in[/tex]
diameter of the larger tire;
D = 2(8.37 in) + 21 in
D = 37.74 in
The circumference of the larger tire;
[tex]C_2 = \pi D\\\\C_2 = 3.142 \times 37.74 \\\\C_2 = 118.58 \ in[/tex]
After one rotation, the larger tire will travel the following distance more than the smaller tire;
[tex]n = \frac{C_2}{C_1} = \frac{118.58}{104.94} = 1.13[/tex]
The distance Janessa traveled on the new tires when her odometer shows she has traveled 23425 miles;
[tex]distance = 1.13 \times 23,425\\\\distance = 26,470.25 \ miles[/tex]
Learn more about tire sizes and distance traveled: https://brainly.com/question/4822144
Evaluate the expression
[3(15+4)2 +2(20+5)2]0
0
5
1
2
0, 5, 5, 1, 2
is evaluate
HELP ME ASAP!!!
Question 3(Multiple Choice Worth 5 points)
(04.04 MC)
If a sprinkler waters 1 over 15 of a lawn in 1 over 3 hour, how much time will it take to water the entire lawn?
5 hours
15 hours
18 hours
45 hours
Answer:
45 hour GIVE BRAINLY PLZ
could you help me with this? its an ss here:
help me i really need it
Answer:
A (0, -4)
Step-by-step explanation:
9x + 3 – 7x + 4
Help me out please?
Answer: The answer is 2x + 7.
Explanation: First, we need to add the numbers:
9x + 3 – 7x + 4
9x + 7 - 7x
And finally, we combine like terms:
9x + 7 - 7x
2x + 7
The graph shows the relationship between time
and the number of soda bottles a machine can
make. Use the points (2,48) and (7,168) to find
the number of soda bottles the machine can make
each minute.
Answer:
24
Step-by-step explanation:
The number of soda bottles the machine can make each minute is the unit rate, slope. To find slope using those two points, use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Identify the points: (2,48) (7,168)
[tex]y_2=168[/tex]
[tex]y_1=48[/tex]
[tex]x_2=7[/tex]
[tex]x_1=2[/tex]
Plug these into the formula then solve:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{168-48}{7-2}[/tex]
[tex]=\frac{120}{5}[/tex]
[tex]=24[/tex]
The slope is 24, and therefore the unit rate. Hence, the machine can make 24 soda bottles each minute.
Simple way
Where you see the point at 48 and 2, it means [tex]\frac{48}{2}[/tex]. So divide
48 ÷ 2 = 24.
Which term of the AP 21, 18, 15 ...... is -81 ?
Given AP is 21 ,18,15,...
First term = 21
Common difference = 18-21 = -3
Let an = -81
We know that
an = a+(n-1)d
⇛21+(n-1)(-3) = -81
⇛ 21-3n+3 = -81
⇛24-3n = -81
⇛ 24+81 = 3n
⇛ 105= 3n
⇛ n = 105/3
⇛ n = 35
35th term of the AP is -81.
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Which term of the AP:3, 8, 13, 18,...,is 78?
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Please help me prove that ED is congruent to BA! I thought I had it right by proving right and vertical angles, but I’m missing something
Step-by-step explanation:
[tex]\overline{DA} \text{ bisects } \overline{EB}[/tex] is given
[tex]\overline{BC} \cong \overline{EC}[/tex] definition of bisect
[tex]\overline{EB} \perp \overline{ED}, \, \overline{EB} \perp \overline{BA}[/tex] are both given
[tex]\angle B, \, \angle E \text{ are right angles}[/tex] definition of perpendicular
[tex]\angle B \cong \angle E[/tex] because all right angles are congruent
[tex]\angle{ACB} \cong \angle{DCE}[/tex] vertical angles are congruent
[tex]\triangle{ACB} \cong \triangle{DCE}[/tex] ASA (angle-side-angle)
[tex]\overline{ED} \cong \overline{BA}[/tex] CPCTC (corresponding parts of congruent triangles are congruent)
Josh drives 504 miles in 8 hours. At the same rate, how many miles would he drive in 5 hours?
Answer:
315 miles
Step-by-step explanation:
The unit rate is 63 miles per hour, and 63×5=315 miles.
[tex]\begin{array}{ccll} miles&hrs\\ \cline{1-2} 504&8\\ x&5 \end{array}\implies \cfrac{504}{x}=\cfrac{8}{5}\implies 2520=8x\implies \cfrac{2520}{8}=x\implies 315=x[/tex]
If DEF and MNO are two triangles such that DE=MN and EF=NO, which of the following would be sufficient to prove that triangles are congruent
Answer:
D. ∠E ≅ ∠N
Step-by-step explanation:
The pair of sides meet at vertex E in ∆DEF and at vertex N in ∆MNO. Since the sides that make up angles E and N are shown congruent, it is sufficient to show ...
∠E ≅ ∠N
Then the SAS congruence postulate can be claimed.
__
Additional comment
The alternative is to show DF ≅ MO. That would allow you to claim SSS congruence. That is not an answer choice.
Describe how to find your x-intercepts ?
0.80x= 28 what is x
please help
Answer: x is nothing.
Step-by-step explanation: The goal is to get x by itself not with the numbers. You just have to solve the equation and whatever you get is equal to X. Example- your problem is 0.80x= 28 which would equal 172 if you're tryna find the solution. X does not matter in your equation and remember x can be any number! I'm not good at explaining so i'm sorry if you have no idea what i'm talking about. I hope this helps!
Your answer is 172.
-Notsonerdy
Evaluate the function h(x) = 13 – x when x= -3,0, and 8.
Answer:
h(-3)=16
h(0)=13
h(8)=5
Step-by-step explanation:
[tex]h( -3) = 13 - ( - 3) = 16 \\ h(0) = 13 - 0 = 13 \\ h(8) = 13 - 8 = 5[/tex]
A sixth grade class collects 176 items for recycling three out of every eight items are cans the rest are bottles how many bottles does the class collect
Answer:
110
Step-by-step explanation:
We know that 5/8 of 176 so the answer is 110.
110 bottles class collect.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A sixth grade class collects 176 items.
Now, three out of every eight items are cans
= (8- 3)
= 5
So, number of bottles class collect
= 176 x 5 / 8
= 22 x 5
= 110
Hence, 110 bottles class collect.
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746 divided by 40 with remainder
Answer:
Quotient: 18; Remainder: 26
Step-by-step explanation:
Please open the PDF file for work.
Hoped this helped.
[tex]GeniusUser[/tex]
Please help i rlly need itttt
Answer:
The value of x is the value where the line crosses the x-axis!
________________________________________________________
Hope this helps!!
Please tell me if I have made a mistake!!
I enjoy learning from them:)
Answer:
x = y - b/m (with the obvious restriction m ≠ 0 )
Step-by-step explanation:
If
y = mx + b
subtracting b from both sides
y - b = mx
dividing both sides by m
y - b/m = x
flipping the sides (to make it look more normal)
x = y - b/m
Casey borrowed $4500 at a 5% interest rate for 4 years.
What was the total interest?
Enter your answer in the box.
Hint: Use the formula I=P*R*T where
I= Interest Earned/Owed
P= Principal
R= Rate
T= Time
PLEASE HURRYYYY!
Find the GCF and LCM for 16 and 24.
Greatest Common Factors (GCF) of 16 and 24 = 8
Least Common Multiple of 16 and 24 = 48
GCF means Greatest Common Factors
Factors of 16 = 1, 2, 8, 4, and 16
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24
Common Factors of 16 and 24 = 1, 2, 4, and 8
Greatest Common Factors (GCF) of 16 and 24 = 8
LCM means Least Common Multiples
Multiples of 16 = 16, 32,48, 54.....
Multiples of 24 = 24, 48, 72....
The Least Common Multiple of 16 and 24 = 48
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My mom walks 1 mile in 14
minutes. If she walked for 56
minutes, how far did she walk?
Answer:
4 miles
Step-by-step explanation
If your mom can walk 1 mile in 14 minutes then 2 miles would take her 28 minutes 3 miles would take her 42 minutes and finally if she walked 4 miles it would take her 56 minutes.
14 + 14 + 14 + 14 = 56
14 x 4 = 56
The segments shown below could form a triangle.
A. True
B. False
False
When completing something like this, the Phythagoream Therom comes into focus. It states that:
A^2 + B^2 = C^2
According to my calculations, A^2 + B^2 = 130 whereas C^2 is 320. This is incorrect and therefore is false.
Some government leaders propose allowing oil companies to drill in currently protected lands that may be rich in oil reserves. Environmental researchers argue that drilling in such lands would be harmful to the surrounding ecosystem. To measure support for drilling in such lands, an oil company representative uses random-digit telephone dialing to contact adults in the region and measure opinion for increased drilling. One question in the survey asks, "Given that an increase in drilling could result in increased tax revenue and additional jobs to the region, would you support a proposal to allow drilling in lands currently protected from drilling?" What type of bias could be most likely affecting the survey results? This is undercoverage bias because some segments of the population will be excluded from the sample. This is response bias because those selected for the survey may not provide truthful opinions about oil drilling. This is voluntary res
The type of bias in this survey is question-wording bias because the question is influencing the response (option D).
Question-wording bias occurs when the words selected in the question influence a specific response. Here is one example:
Do you believe a cruel practice such as bullfighting should be forbidden?In this question, the use of the word cruel qualifies bullfighting as negative, and therefore in most cases, people will answer that bullfighting should be forbidden.
This effect occurs in the question for this survey because the section given that an increase in drilling could result in increased tax revenue and additional jobs to the region indirectly states drilling is positive and therefore influences the response of those surveyed.
Note: This question is incomplete because some of the options are missing; here are the complete options:
What type of bias could be most likely affecting the survey results?
A. This is undercoverage bias because some segments of the population will be excluded from the sample.
B. This is response bias because those selected for the survey may not provide truthful opinions about oil drilling.
C. This is voluntary response bias because those most passionate about drilling will be more likely to register an opinion.
D. This is question-wording bias because the information given at the start of the question may lead those surveyed towards a desired response.
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Write an equation for the situation: Kristian has $200 which is two times Alejo's money plus $20.
Answer:
x= 2y + 20
Step-by-step explanation:
we could say kristian and alejo, Bob and Bill, shelled and Jackie or just about any other two words so let's call them x any y. kristian is x and also is y.
so kristian (x) has twice as much money plus another 20.
this means x has 2 times plus 20 more than y.
so x= 2y + 20
Suraj took a slice of pizza from the freezer and put it in the oven. The pizza’s temperature (in degrees celsius) as a function of time (in minutes) is graphed. What was the pizza’s temperature after 2 minutes?
For this case, the first thing we should do is write the linear function that best suits the table.
In this case we have the following function:
y = 7.5x - 5
C = 7.5t-5
For C = 100 we have:
100 = 7.5t-5
We clear the time:
t = (100 + 5) / (7.5)
t = 14
Answer:
it did take the pizza to reach 100 degrees Celsius about 14 minutes
Based on the data given in the frequency table below, does a greater percent of eleventh
or twelfth graders surveyed like tennis? Use conditional relative frequencies to support
your answer.
Like Tennis
Grade
Yes
No
Total
Eleventh
45
50
95
Twelfth
62
28
90
Total
107
78
185
Rounded to the nearest thousandth, the conditional relative frequency that an eleventh
grader likes tennis is
Rounded to the nearest thousandth, the conditional relative frequency that a twelfth
grader likes tennis is
Since
% is less than %, a greater percent of (select)
like tennis.
Answer: the answers vary since mine and urs are different, so these are my answers: 0.48, 0.63, 48, 63, twelth graders. youll have too think about it a lil bit, sry
Mark brainliest pls and also look at picture if u don't understand
Step-by-step explanation:
Yw :) :D
Stop looking up answers on brainly
Maya solved 1/4 of a crossword puzzle before dinner and a part of it after dinner. If Maya solved 3/4 of the crossword in all, what fraction of the puzzle did she solve after dinner?
Choose the equation that matches the word problem.
Answer:2/4
Step-by-step explanation: you would just subtract 3/4 by 1/4 to get 2/4
De cuántas formas pueden mezclarse los siete colores del arco iris tomándolos de tres en tres?
Answer:
hi
Step-by-step explanation:
1+1=2